LMFDB - Embedded newform 1064.2.q.k.305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			305.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.k.457.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 + 0.507306i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.32843 + 2.30090i) q^{9} +O(q^{10})$	\(q+(-0.292893 + 0.507306i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.32843 + 2.30090i) q^{9} +(-2.62132 + 4.54026i) q^{11} -0.585786 q^{13} -0.585786 q^{15} +(0.585786 - 1.01461i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-0.585786 + 1.43488i) q^{21} +(-0.792893 - 1.37333i) q^{23} +(2.00000 - 3.46410i) q^{25} -3.31371 q^{27} -6.58579 q^{29} +(-3.70711 + 6.42090i) q^{31} +(-1.53553 - 2.65962i) q^{33} +(1.62132 + 2.09077i) q^{35} +(4.70711 + 8.15295i) q^{37} +(0.171573 - 0.297173i) q^{39} +5.65685 q^{41} +5.24264 q^{43} +(-1.32843 + 2.30090i) q^{45} +(-3.62132 - 6.27231i) q^{47} +(6.74264 - 1.88064i) q^{49} +(0.343146 + 0.594346i) q^{51} +(1.29289 - 2.23936i) q^{53} -5.24264 q^{55} -0.585786 q^{57} +(-2.41421 + 4.18154i) q^{59} +(2.50000 + 4.33013i) q^{61} +(4.30761 + 5.55487i) q^{63} +(-0.292893 - 0.507306i) q^{65} +(-4.41421 + 7.64564i) q^{67} +0.928932 q^{69} -16.2426 q^{71} +(3.50000 - 6.06218i) q^{73} +(1.17157 + 2.02922i) q^{75} +(-5.24264 + 12.8418i) q^{77} +(7.94975 + 13.7694i) q^{79} +(-3.01472 + 5.22165i) q^{81} -4.89949 q^{83} +1.17157 q^{85} +(1.92893 - 3.34101i) q^{87} +(8.77817 + 15.2042i) q^{89} +(-1.53553 + 0.210133i) q^{91} +(-2.17157 - 3.76127i) q^{93} +(-0.500000 + 0.866025i) q^{95} +5.65685 q^{97} -13.9289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 2 q^{11} - 8 q^{13} - 8 q^{15} + 8 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{23} + 8 q^{25} + 32 q^{27} - 32 q^{29} - 12 q^{31} + 8 q^{33} - 2 q^{35} + 16 q^{37} + 12 q^{39} + 4 q^{43} + 6 q^{45} - 6 q^{47} + 10 q^{49} + 24 q^{51} + 8 q^{53} - 4 q^{55} - 8 q^{57} - 4 q^{59} + 10 q^{61} + 54 q^{63} - 4 q^{65} - 12 q^{67} + 32 q^{69} - 48 q^{71} + 14 q^{73} + 16 q^{75} - 4 q^{77} + 12 q^{79} - 46 q^{81} + 20 q^{83} + 16 q^{85} + 36 q^{87} + 4 q^{89} + 8 q^{91} - 20 q^{93} - 2 q^{95} - 84 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 2 * q^11 - 8 * q^13 - 8 * q^15 + 8 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^23 + 8 * q^25 + 32 * q^27 - 32 * q^29 - 12 * q^31 + 8 * q^33 - 2 * q^35 + 16 * q^37 + 12 * q^39 + 4 * q^43 + 6 * q^45 - 6 * q^47 + 10 * q^49 + 24 * q^51 + 8 * q^53 - 4 * q^55 - 8 * q^57 - 4 * q^59 + 10 * q^61 + 54 * q^63 - 4 * q^65 - 12 * q^67 + 32 * q^69 - 48 * q^71 + 14 * q^73 + 16 * q^75 - 4 * q^77 + 12 * q^79 - 46 * q^81 + 20 * q^83 + 16 * q^85 + 36 * q^87 + 4 * q^89 + 8 * q^91 - 20 * q^93 - 2 * q^95 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.292893	+	0.507306i	−0.169102	+	0.292893i	−0.938104	−	0.346353i	$-0.887420\pi$
$3$	−0.292893	+	0.507306i	−0.169102	+	0.292893i	0.769002	+	0.639246i	$0.220753\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$		0			0
$9$	1.32843	+	2.30090i	0.442809	+	0.766968i
$10$		0			0
$11$	−2.62132	+	4.54026i	−0.790358	+	1.36894i	0.135388	+	0.990793i	$0.456772\pi$
$11$	−2.62132	+	4.54026i	−0.790358	+	1.36894i	−0.925745	+	0.378147i	$0.876561\pi$
$12$		0			0
$13$	−0.585786			−0.162468			−0.0812340	−	0.996695i	$-0.525886\pi$
$13$	−0.585786			−0.162468			−0.0812340	+	0.996695i	$0.525886\pi$
$14$		0			0
$15$	−0.585786			−0.151249
$16$		0			0
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	−0.786203	−	0.617968i	$-0.787956\pi$
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	0.928278	+	0.371888i	$0.121290\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$		0			0
$21$	−0.585786	+	1.43488i	−0.127829	+	0.313116i
$22$		0			0
$23$	−0.792893	−	1.37333i	−0.165330	−	0.286359i	0.771443	−	0.636299i	$-0.219535\pi$
$23$	−0.792893	−	1.37333i	−0.165330	−	0.286359i	−0.936772	+	0.349939i	$0.886202\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−3.31371			−0.637723
$28$		0			0
$29$	−6.58579			−1.22295			−0.611475	−	0.791264i	$-0.709423\pi$
$29$	−6.58579			−1.22295			−0.611475	+	0.791264i	$0.709423\pi$
$30$		0			0
$31$	−3.70711	+	6.42090i	−0.665816	+	1.15323i	0.313247	+	0.949672i	$0.398583\pi$
$31$	−3.70711	+	6.42090i	−0.665816	+	1.15323i	−0.979063	+	0.203556i	$0.934750\pi$
$32$		0			0
$33$	−1.53553	−	2.65962i	−0.267302	−	0.462981i
$34$		0			0
$35$	1.62132	+	2.09077i	0.274053	+	0.353405i
$36$		0			0
$37$	4.70711	+	8.15295i	0.773844	+	1.34034i	0.935442	+	0.353480i	$0.115002\pi$
$37$	4.70711	+	8.15295i	0.773844	+	1.34034i	−0.161599	+	0.986857i	$0.551665\pi$
$38$		0			0
$39$	0.171573	−	0.297173i	0.0274736	−	0.0475858i
$40$		0			0
$41$	5.65685			0.883452			0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685			0.883452			0.441726	+	0.897150i	$0.354366\pi$
$42$		0			0
$43$	5.24264			0.799495			0.399748	−	0.916625i	$-0.369098\pi$
$43$	5.24264			0.799495			0.399748	+	0.916625i	$0.369098\pi$
$44$		0			0
$45$	−1.32843	+	2.30090i	−0.198030	+	0.342998i
$46$		0			0
$47$	−3.62132	−	6.27231i	−0.528224	−	0.914911i	−0.999459	−	0.0329027i	$-0.989525\pi$
$47$	−3.62132	−	6.27231i	−0.528224	−	0.914911i	0.471235	−	0.882008i	$-0.343808\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		0			0
$51$	0.343146	+	0.594346i	0.0480500	+	0.0832251i
$52$		0			0
$53$	1.29289	−	2.23936i	0.177593	−	0.307599i	−0.763463	−	0.645852i	$-0.776502\pi$
$53$	1.29289	−	2.23936i	0.177593	−	0.307599i	0.941055	+	0.338252i	$0.109836\pi$
$54$		0			0
$55$	−5.24264			−0.706918
$56$		0			0
$57$	−0.585786			−0.0775893
$58$		0			0
$59$	−2.41421	+	4.18154i	−0.314304	+	0.544390i	−0.979289	−	0.202466i	$-0.935104\pi$
$59$	−2.41421	+	4.18154i	−0.314304	+	0.544390i	0.664985	+	0.746856i	$0.268438\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		0			0
$63$	4.30761	+	5.55487i	0.542708	+	0.699848i
$64$		0			0
$65$	−0.292893	−	0.507306i	−0.0363289	−	0.0629236i
$66$		0			0
$67$	−4.41421	+	7.64564i	−0.539282	+	0.934064i	0.459661	+	0.888095i	$0.347971\pi$
$67$	−4.41421	+	7.64564i	−0.539282	+	0.934064i	−0.998943	+	0.0459693i	$0.985362\pi$
$68$		0			0
$69$	0.928932			0.111830
$70$		0			0
$71$	−16.2426			−1.92765			−0.963823	−	0.266542i	$-0.914119\pi$
$71$	−16.2426			−1.92765			−0.963823	+	0.266542i	$0.914119\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$	1.17157	+	2.02922i	0.135282	+	0.234315i
$76$		0			0
$77$	−5.24264	+	12.8418i	−0.597454	+	1.46346i
$78$		0			0
$79$	7.94975	+	13.7694i	0.894416	+	1.54917i	0.834525	+	0.550970i	$0.185742\pi$
$79$	7.94975	+	13.7694i	0.894416	+	1.54917i	0.0598913	+	0.998205i	$0.480925\pi$
$80$		0			0
$81$	−3.01472	+	5.22165i	−0.334969	+	0.580183i
$82$		0			0
$83$	−4.89949			−0.537789			−0.268895	−	0.963170i	$-0.586658\pi$
$83$	−4.89949			−0.537789			−0.268895	+	0.963170i	$0.586658\pi$
$84$		0			0
$85$	1.17157			0.127075
$86$		0			0
$87$	1.92893	−	3.34101i	0.206803	−	0.358194i
$88$		0			0
$89$	8.77817	+	15.2042i	0.930485	+	1.61165i	0.782494	+	0.622658i	$0.213947\pi$
$89$	8.77817	+	15.2042i	0.930485	+	1.61165i	0.147990	+	0.988989i	$0.452720\pi$
$90$		0			0
$91$	−1.53553	+	0.210133i	−0.160968	+	0.0220279i
$92$		0			0
$93$	−2.17157	−	3.76127i	−0.225182	−	0.390026i
$94$		0			0
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$		0			0
$97$	5.65685			0.574367			0.287183	−	0.957876i	$-0.407281\pi$
$97$	5.65685			0.574367			0.287183	+	0.957876i	$0.407281\pi$
$98$		0			0
$99$	−13.9289			−1.39991
$100$		0			0
$101$	7.74264	−	13.4106i	0.770422	−	1.33441i	−0.166911	−	0.985972i	$-0.553379\pi$
$101$	7.74264	−	13.4106i	0.770422	−	1.33441i	0.937332	−	0.348437i	$-0.113288\pi$
$102$		0			0
$103$	−6.82843	−	11.8272i	−0.672825	−	1.16537i	−0.977100	−	0.212783i	$-0.931747\pi$
$103$	−6.82843	−	11.8272i	−0.672825	−	1.16537i	0.304275	−	0.952584i	$-0.401586\pi$
$104$		0			0
$105$	−1.53553	+	0.210133i	−0.149853	+	0.0205069i
$106$		0			0
$107$	−1.46447	−	2.53653i	−0.141575	−	0.245216i	0.786515	−	0.617572i	$-0.211883\pi$
$107$	−1.46447	−	2.53653i	−0.141575	−	0.245216i	−0.928090	+	0.372356i	$0.878550\pi$
$108$		0			0
$109$	−1.65685	+	2.86976i	−0.158698	+	0.274873i	−0.934399	−	0.356227i	$-0.884063\pi$
$109$	−1.65685	+	2.86976i	−0.158698	+	0.274873i	0.775702	+	0.631100i	$0.217396\pi$
$110$		0			0
$111$	−5.51472			−0.523434
$112$		0			0
$113$	−3.07107			−0.288902			−0.144451	−	0.989512i	$-0.546142\pi$
$113$	−3.07107			−0.288902			−0.144451	+	0.989512i	$0.546142\pi$
$114$		0			0
$115$	0.792893	−	1.37333i	0.0739377	−	0.128064i
$116$		0			0
$117$	−0.778175	−	1.34784i	−0.0719423	−	0.124608i
$118$		0			0
$119$	1.17157	−	2.86976i	0.107398	−	0.263070i
$120$		0			0
$121$	−8.24264	−	14.2767i	−0.749331	−	1.29788i
$122$		0			0
$123$	−1.65685	+	2.86976i	−0.149394	+	0.258757i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	11.5563			1.02546			0.512730	−	0.858550i	$-0.328634\pi$
$127$	11.5563			1.02546			0.512730	+	0.858550i	$0.328634\pi$
$128$		0			0
$129$	−1.53553	+	2.65962i	−0.135196	+	0.234167i
$130$		0			0
$131$	4.82843	+	8.36308i	0.421862	+	0.730686i	0.996122	−	0.0879872i	$-0.0280435\pi$
$131$	4.82843	+	8.36308i	0.421862	+	0.730686i	−0.574260	+	0.818673i	$0.694710\pi$
$132$		0			0
$133$	1.62132	+	2.09077i	0.140586	+	0.181293i
$134$		0			0
$135$	−1.65685	−	2.86976i	−0.142599	−	0.246989i
$136$		0			0
$137$	5.32843	−	9.22911i	0.455238	−	0.788496i	−0.543464	−	0.839433i	$-0.682887\pi$
$137$	5.32843	−	9.22911i	0.455238	−	0.788496i	0.998702	+	0.0509369i	$0.0162208\pi$
$138$		0			0
$139$	12.5563			1.06502			0.532508	−	0.846425i	$-0.321250\pi$
$139$	12.5563			1.06502			0.532508	+	0.846425i	$0.321250\pi$
$140$		0			0
$141$	4.24264			0.357295
$142$		0			0
$143$	1.53553	−	2.65962i	0.128408	−	0.222409i
$144$		0			0
$145$	−3.29289	−	5.70346i	−0.273460	−	0.473646i
$146$		0			0
$147$	−1.02082	+	3.97141i	−0.0841954	+	0.327556i
$148$		0			0
$149$	−2.32843	−	4.03295i	−0.190752	−	0.330392i	0.754748	−	0.656015i	$-0.227759\pi$
$149$	−2.32843	−	4.03295i	−0.190752	−	0.330392i	−0.945500	+	0.325623i	$0.894426\pi$
$150$		0			0
$151$	2.82843	−	4.89898i	0.230174	−	0.398673i	−0.727685	−	0.685911i	$-0.759404\pi$
$151$	2.82843	−	4.89898i	0.230174	−	0.398673i	0.957859	+	0.287238i	$0.0927371\pi$
$152$		0			0
$153$	3.11270			0.251647
$154$		0			0
$155$	−7.41421			−0.595524
$156$		0			0
$157$	12.1569	−	21.0563i	0.970223	−	1.68047i	0.275347	−	0.961345i	$-0.411207\pi$
$157$	12.1569	−	21.0563i	0.970223	−	1.68047i	0.694876	−	0.719130i	$-0.255459\pi$
$158$		0			0
$159$	0.757359	+	1.31178i	0.0600625	+	0.104031i
$160$		0			0
$161$	−2.57107	−	3.31552i	−0.202629	−	0.261299i
$162$		0			0
$163$	0.0355339	+	0.0615465i	0.00278323	+	0.00482070i	0.867414	−	0.497588i	$-0.165781\pi$
$163$	0.0355339	+	0.0615465i	0.00278323	+	0.00482070i	−0.864630	+	0.502408i	$0.832447\pi$
$164$		0			0
$165$	1.53553	−	2.65962i	0.119541	−	0.207051i
$166$		0			0
$167$	21.4142			1.65708			0.828541	−	0.559929i	$-0.189171\pi$
$167$	21.4142			1.65708			0.828541	+	0.559929i	$0.189171\pi$
$168$		0			0
$169$	−12.6569			−0.973604
$170$		0			0
$171$	−1.32843	+	2.30090i	−0.101587	+	0.175954i
$172$		0			0
$173$	−0.828427	−	1.43488i	−0.0629841	−	0.109092i	0.832814	−	0.553553i	$-0.186728\pi$
$173$	−0.828427	−	1.43488i	−0.0629841	−	0.109092i	−0.895798	+	0.444461i	$0.853395\pi$
$174$		0			0
$175$	4.00000	−	9.79796i	0.302372	−	0.740656i
$176$		0			0
$177$	−1.41421	−	2.44949i	−0.106299	−	0.184115i
$178$		0			0
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	−0.600841	−	0.799369i	$-0.705167\pi$
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	0.992694	+	0.120659i	$0.0385007\pi$
$180$		0			0
$181$	10.7279			0.797400			0.398700	−	0.917081i	$-0.369461\pi$
$181$	10.7279			0.797400			0.398700	+	0.917081i	$0.369461\pi$
$182$		0			0
$183$	−2.92893			−0.216513
$184$		0			0
$185$	−4.70711	+	8.15295i	−0.346073	+	0.599417i
$186$		0			0
$187$	3.07107	+	5.31925i	0.224579	+	0.388982i
$188$		0			0
$189$	−8.68629	+	1.18869i	−0.631835	+	0.0864646i
$190$		0			0
$191$	−0.378680	−	0.655892i	−0.0274003	−	0.0474587i	0.852000	−	0.523542i	$-0.175390\pi$
$191$	−0.378680	−	0.655892i	−0.0274003	−	0.0474587i	−0.879400	+	0.476083i	$0.842056\pi$
$192$		0			0
$193$	3.12132	−	5.40629i	0.224678	−	0.389153i	−0.731545	−	0.681793i	$-0.761200\pi$
$193$	3.12132	−	5.40629i	0.224678	−	0.389153i	0.956223	+	0.292640i	$0.0945338\pi$
$194$		0			0
$195$	0.343146			0.0245732
$196$		0			0
$197$	−17.4853			−1.24577			−0.622887	−	0.782312i	$-0.714041\pi$
$197$	−17.4853			−1.24577			−0.622887	+	0.782312i	$0.714041\pi$
$198$		0			0
$199$	6.03553	−	10.4539i	0.427848	−	0.741054i	−0.568834	−	0.822452i	$-0.692605\pi$
$199$	6.03553	−	10.4539i	0.427848	−	0.741054i	0.996682	+	0.0813985i	$0.0259386\pi$
$200$		0			0
$201$	−2.58579	−	4.47871i	−0.182387	−	0.315904i
$202$		0			0
$203$	−17.2635	+	2.36245i	−1.21166	+	0.165811i
$204$		0			0
$205$	2.82843	+	4.89898i	0.197546	+	0.342160i
$206$		0			0
$207$	2.10660	−	3.64874i	0.146419	−	0.253605i
$208$		0			0
$209$	−5.24264			−0.362641
$210$		0			0
$211$	−16.1421			−1.11127			−0.555635	−	0.831426i	$-0.687525\pi$
$211$	−16.1421			−1.11127			−0.555635	+	0.831426i	$0.687525\pi$
$212$		0			0
$213$	4.75736	−	8.23999i	0.325969	−	0.564595i
$214$		0			0
$215$	2.62132	+	4.54026i	0.178773	+	0.309643i
$216$		0			0
$217$	−7.41421	+	18.1610i	−0.503310	+	1.23285i
$218$		0			0
$219$	2.05025	+	3.55114i	0.138543	+	0.239964i
$220$		0			0
$221$	−0.343146	+	0.594346i	−0.0230825	+	0.0399800i
$222$		0			0
$223$	−7.75736			−0.519471			−0.259736	−	0.965680i	$-0.583635\pi$
$223$	−7.75736			−0.519471			−0.259736	+	0.965680i	$0.583635\pi$
$224$		0			0
$225$	10.6274			0.708494
$226$		0			0
$227$	0.707107	−	1.22474i	0.0469323	−	0.0812892i	−0.841605	−	0.540094i	$-0.818389\pi$
$227$	0.707107	−	1.22474i	0.0469323	−	0.0812892i	0.888537	+	0.458804i	$0.151722\pi$
$228$		0			0
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$		0			0
$231$	−4.97918	−	6.42090i	−0.327606	−	0.422464i
$232$		0			0
$233$	8.82843	+	15.2913i	0.578369	+	1.00177i	0.995667	+	0.0929952i	$0.0296441\pi$
$233$	8.82843	+	15.2913i	0.578369	+	1.00177i	−0.417297	+	0.908770i	$0.637023\pi$
$234$		0			0
$235$	3.62132	−	6.27231i	0.236229	−	0.409160i
$236$		0			0
$237$	−9.31371			−0.604990
$238$		0			0
$239$	−15.6569			−1.01276			−0.506379	−	0.862311i	$-0.669016\pi$
$239$	−15.6569			−1.01276			−0.506379	+	0.862311i	$0.669016\pi$
$240$		0			0
$241$	8.36396	−	14.4868i	0.538770	−	0.933177i	−0.460201	−	0.887815i	$-0.652222\pi$
$241$	8.36396	−	14.4868i	0.538770	−	0.933177i	0.998971	−	0.0453622i	$-0.0144442\pi$
$242$		0			0
$243$	−6.73654	−	11.6680i	−0.432150	−	0.748505i
$244$		0			0
$245$	5.00000	+	4.89898i	0.319438	+	0.312984i
$246$		0			0
$247$	−0.292893	−	0.507306i	−0.0186363	−	0.0322791i
$248$		0			0
$249$	1.43503	−	2.48554i	0.0909413	−	0.157515i
$250$		0			0
$251$	20.2132			1.27585			0.637923	−	0.770100i	$-0.279794\pi$
$251$	20.2132			1.27585			0.637923	+	0.770100i	$0.279794\pi$
$252$		0			0
$253$	8.31371			0.522678
$254$		0			0
$255$	−0.343146	+	0.594346i	−0.0214886	+	0.0372194i
$256$		0			0
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$		0			0
$259$	15.2635	+	19.6830i	0.948425	+	1.22304i
$260$		0			0
$261$	−8.74874	−	15.1533i	−0.541533	−	0.937963i
$262$		0			0
$263$	13.4142	−	23.2341i	0.827156	−	1.43268i	−0.0731046	−	0.997324i	$-0.523291\pi$
$263$	13.4142	−	23.2341i	0.827156	−	1.43268i	0.900260	−	0.435352i	$-0.143376\pi$
$264$		0			0
$265$	2.58579			0.158844
$266$		0			0
$267$	−10.2843			−0.629387
$268$		0			0
$269$	8.00000	−	13.8564i	0.487769	−	0.844840i	−0.512132	−	0.858906i	$-0.671144\pi$
$269$	8.00000	−	13.8564i	0.487769	−	0.844840i	0.999901	+	0.0140665i	$0.00447764\pi$
$270$		0			0
$271$	−13.8640	−	24.0131i	−0.842176	−	1.45869i	−0.888052	−	0.459744i	$-0.847941\pi$
$271$	−13.8640	−	24.0131i	−0.842176	−	1.45869i	0.0458759	−	0.998947i	$-0.485392\pi$
$272$		0			0
$273$	0.343146	−	0.840532i	0.0207681	−	0.0508713i
$274$		0			0
$275$	10.4853	+	18.1610i	0.632286	+	1.09515i
$276$		0			0
$277$	−2.98528	+	5.17066i	−0.179368	+	0.310675i	−0.941664	−	0.336554i	$-0.890739\pi$
$277$	−2.98528	+	5.17066i	−0.179368	+	0.310675i	0.762296	+	0.647228i	$0.224072\pi$
$278$		0			0
$279$	−19.6985			−1.17932
$280$		0			0
$281$	1.89949			0.113314			0.0566572	−	0.998394i	$-0.481956\pi$
$281$	1.89949			0.113314			0.0566572	+	0.998394i	$0.481956\pi$
$282$		0			0
$283$	8.27817	−	14.3382i	0.492086	−	0.852319i	−0.507872	−	0.861433i	$-0.669568\pi$
$283$	8.27817	−	14.3382i	0.492086	−	0.852319i	0.999958	+	0.00911386i	$0.00290107\pi$
$284$		0			0
$285$	−0.292893	−	0.507306i	−0.0173495	−	0.0300502i
$286$		0			0
$287$	14.8284	−	2.02922i	0.875294	−	0.119781i
$288$		0			0
$289$	7.81371	+	13.5337i	0.459630	+	0.796102i
$290$		0			0
$291$	−1.65685	+	2.86976i	−0.0971265	+	0.168228i
$292$		0			0
$293$	−1.65685			−0.0967945			−0.0483972	−	0.998828i	$-0.515411\pi$
$293$	−1.65685			−0.0967945			−0.0483972	+	0.998828i	$0.515411\pi$
$294$		0			0
$295$	−4.82843			−0.281122
$296$		0			0
$297$	8.68629	−	15.0451i	0.504030	−	0.873005i
$298$		0			0
$299$	0.464466	+	0.804479i	0.0268608	+	0.0465242i
$300$		0			0
$301$	13.7426	−	1.88064i	0.792113	−	0.108398i
$302$		0			0
$303$	4.53553	+	7.85578i	0.260560	+	0.451302i
$304$		0			0
$305$	−2.50000	+	4.33013i	−0.143150	+	0.247942i
$306$		0			0
$307$	−26.6274			−1.51971			−0.759853	−	0.650094i	$-0.774729\pi$
$307$	−26.6274			−1.51971			−0.759853	+	0.650094i	$0.774729\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$		0			0
$313$	13.5711	+	23.5058i	0.767082	+	1.32863i	0.939139	+	0.343538i	$0.111625\pi$
$313$	13.5711	+	23.5058i	0.767082	+	1.32863i	−0.172057	+	0.985087i	$0.555041\pi$
$314$		0			0
$315$	−2.65685	+	6.50794i	−0.149697	+	0.366681i
$316$		0			0
$317$	0.878680	+	1.52192i	0.0493516	+	0.0854794i	0.889646	−	0.456651i	$-0.150951\pi$
$317$	0.878680	+	1.52192i	0.0493516	+	0.0854794i	−0.840294	+	0.542130i	$0.817618\pi$
$318$		0			0
$319$	17.2635	−	29.9012i	0.966568	−	1.67414i
$320$		0			0
$321$	1.71573			0.0957626
$322$		0			0
$323$	1.17157			0.0651881
$324$		0			0
$325$	−1.17157	+	2.02922i	−0.0649872	+	0.112561i
$326$		0			0
$327$	−0.970563	−	1.68106i	−0.0536722	−	0.0929631i
$328$		0			0
$329$	−11.7426	−	15.1427i	−0.647393	−	0.834844i
$330$		0			0
$331$	0.757359	+	1.31178i	0.0416282	+	0.0721022i	0.886089	−	0.463515i	$-0.153412\pi$
$331$	0.757359	+	1.31178i	0.0416282	+	0.0721022i	−0.844461	+	0.535618i	$0.820079\pi$
$332$		0			0
$333$	−12.5061	+	21.6612i	−0.685330	+	1.18703i
$334$		0			0
$335$	−8.82843			−0.482349
$336$		0			0
$337$	−9.07107			−0.494133			−0.247066	−	0.968999i	$-0.579467\pi$
$337$	−9.07107			−0.494133			−0.247066	+	0.968999i	$0.579467\pi$
$338$		0			0
$339$	0.899495	−	1.55797i	0.0488539	−	0.0846174i
$340$		0			0
$341$	−19.4350	−	33.6625i	−1.05247	−	1.82292i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$	0.464466	+	0.804479i	0.0250060	+	0.0433117i
$346$		0			0
$347$	−4.79289	+	8.30153i	−0.257296	+	0.445650i	−0.965517	−	0.260341i	$-0.916165\pi$
$347$	−4.79289	+	8.30153i	−0.257296	+	0.445650i	0.708221	+	0.705991i	$0.249498\pi$
$348$		0			0
$349$	−5.65685			−0.302804			−0.151402	−	0.988472i	$-0.548379\pi$
$349$	−5.65685			−0.302804			−0.151402	+	0.988472i	$0.548379\pi$
$350$		0			0
$351$	1.94113			0.103610
$352$		0			0
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	−8.12132	−	14.0665i	−0.431035	−	0.746574i
$356$		0			0
$357$	1.11270	+	1.43488i	0.0588902	+	0.0759418i
$358$		0			0
$359$	11.3492	+	19.6575i	0.598990	+	1.03748i	0.992970	+	0.118362i	$0.0377645\pi$
$359$	11.3492	+	19.6575i	0.598990	+	1.03748i	−0.393980	+	0.919119i	$0.628902\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$	9.65685			0.506853
$364$		0			0
$365$	7.00000			0.366397
$366$		0			0
$367$	14.3137	−	24.7921i	0.747170	−	1.29414i	−0.202005	−	0.979385i	$-0.564746\pi$
$367$	14.3137	−	24.7921i	0.747170	−	1.29414i	0.949174	−	0.314751i	$-0.101921\pi$
$368$		0			0
$369$	7.51472	+	13.0159i	0.391201	+	0.677579i
$370$		0			0
$371$	2.58579	−	6.33386i	0.134247	−	0.328837i
$372$		0			0
$373$	8.82843	+	15.2913i	0.457119	+	0.791753i	0.998807	−	0.0488265i	$-0.0155481\pi$
$373$	8.82843	+	15.2913i	0.457119	+	0.791753i	−0.541689	+	0.840579i	$0.682215\pi$
$374$		0			0
$375$	−2.63604	+	4.56575i	−0.136124	+	0.235774i
$376$		0			0
$377$	3.85786			0.198690
$378$		0			0
$379$	15.4142			0.791775			0.395887	−	0.918299i	$-0.370437\pi$
$379$	15.4142			0.791775			0.395887	+	0.918299i	$0.370437\pi$
$380$		0			0
$381$	−3.38478	+	5.86260i	−0.173407	+	0.300350i
$382$		0			0
$383$	6.12132	+	10.6024i	0.312785	+	0.541759i	0.978964	−	0.204032i	$-0.0654048\pi$
$383$	6.12132	+	10.6024i	0.312785	+	0.541759i	−0.666179	+	0.745792i	$0.732071\pi$
$384$		0			0
$385$	−13.7426	+	1.88064i	−0.700390	+	0.0958462i
$386$		0			0
$387$	6.96447	+	12.0628i	0.354024	+	0.613187i
$388$		0			0
$389$	−3.65685	+	6.33386i	−0.185410	+	0.321139i	−0.943715	−	0.330761i	$-0.892695\pi$
$389$	−3.65685	+	6.33386i	−0.185410	+	0.321139i	0.758305	+	0.651900i	$0.226028\pi$
$390$		0			0
$391$	−1.85786			−0.0939562
$392$		0			0
$393$	−5.65685			−0.285351
$394$		0			0
$395$	−7.94975	+	13.7694i	−0.399995	+	0.692812i
$396$		0			0
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	0.963786	−	0.266678i	$-0.0859261\pi$
$397$	5.00000	+	8.66025i	0.250943	+	0.434646i	−0.712843	+	0.701324i	$0.752593\pi$
$398$		0			0
$399$	−1.53553	+	0.210133i	−0.0768728	+	0.0105198i
$400$		0			0
$401$	−18.3137	−	31.7203i	−0.914543	−	1.58403i	−0.807569	−	0.589773i	$-0.799217\pi$
$401$	−18.3137	−	31.7203i	−0.914543	−	1.58403i	−0.106974	−	0.994262i	$-0.534116\pi$
$402$		0			0
$403$	2.17157	−	3.76127i	0.108174	−	0.187362i
$404$		0			0
$405$	−6.02944			−0.299605
$406$		0			0
$407$	−49.3553			−2.44645
$408$		0			0
$409$	3.34315	−	5.79050i	0.165308	−	0.286322i	−0.771457	−	0.636282i	$-0.780472\pi$
$409$	3.34315	−	5.79050i	0.165308	−	0.286322i	0.936765	+	0.349960i	$0.113805\pi$
$410$		0			0
$411$	3.12132	+	5.40629i	0.153963	+	0.266672i
$412$		0			0
$413$	−4.82843	+	11.8272i	−0.237591	+	0.581978i
$414$		0			0
$415$	−2.44975	−	4.24309i	−0.120253	−	0.208285i
$416$		0			0
$417$	−3.67767	+	6.36991i	−0.180096	+	0.311936i
$418$		0			0
$419$	28.6985			1.40201			0.701006	−	0.713155i	$-0.252734\pi$
$419$	28.6985			1.40201			0.701006	+	0.713155i	$0.252734\pi$
$420$		0			0
$421$	−27.4142			−1.33609			−0.668044	−	0.744122i	$-0.732868\pi$
$421$	−27.4142			−1.33609			−0.668044	+	0.744122i	$0.732868\pi$
$422$		0			0
$423$	9.62132	−	16.6646i	0.467805	−	0.810261i
$424$		0			0
$425$	−2.34315	−	4.05845i	−0.113659	−	0.196864i
$426$		0			0
$427$	8.10660	+	10.4539i	0.392306	+	0.505897i
$428$		0			0
$429$	0.899495	+	1.55797i	0.0434280	+	0.0752195i
$430$		0			0
$431$	−2.94975	+	5.10911i	−0.142084	+	0.246097i	−0.928281	−	0.371879i	$-0.878714\pi$
$431$	−2.94975	+	5.10911i	−0.142084	+	0.246097i	0.786197	+	0.617976i	$0.212047\pi$
$432$		0			0
$433$	12.0000			0.576683			0.288342	−	0.957528i	$-0.406896\pi$
$433$	12.0000			0.576683			0.288342	+	0.957528i	$0.406896\pi$
$434$		0			0
$435$	3.85786			0.184970
$436$		0			0
$437$	0.792893	−	1.37333i	0.0379292	−	0.0656953i
$438$		0			0
$439$	−4.75736	−	8.23999i	−0.227056	−	0.393273i	0.729878	−	0.683577i	$-0.239577\pi$
$439$	−4.75736	−	8.23999i	−0.227056	−	0.393273i	−0.956934	+	0.290304i	$0.906243\pi$
$440$		0			0
$441$	13.2843	+	13.0159i	0.632584	+	0.619804i
$442$		0			0
$443$	19.6569	+	34.0467i	0.933925	+	1.61761i	0.776539	+	0.630069i	$0.216973\pi$
$443$	19.6569	+	34.0467i	0.933925	+	1.61761i	0.157386	+	0.987537i	$0.449693\pi$
$444$		0			0
$445$	−8.77817	+	15.2042i	−0.416125	+	0.720750i
$446$		0			0
$447$	2.72792			0.129026
$448$		0			0
$449$	−14.6274			−0.690310			−0.345155	−	0.938546i	$-0.612174\pi$
$449$	−14.6274			−0.690310			−0.345155	+	0.938546i	$0.612174\pi$
$450$		0			0
$451$	−14.8284	+	25.6836i	−0.698243	+	1.20939i
$452$		0			0
$453$	1.65685	+	2.86976i	0.0778458	+	0.134833i
$454$		0			0
$455$	−0.949747	−	1.22474i	−0.0445248	−	0.0574169i
$456$		0			0
$457$	−0.0857864	−	0.148586i	−0.00401292	−	0.00695058i	0.864012	−	0.503471i	$-0.167944\pi$
$457$	−0.0857864	−	0.148586i	−0.00401292	−	0.00695058i	−0.868025	+	0.496521i	$0.834611\pi$
$458$		0			0
$459$	−1.94113	+	3.36213i	−0.0906040	+	0.156931i
$460$		0			0
$461$	−28.7990			−1.34130			−0.670651	−	0.741773i	$-0.733985\pi$
$461$	−28.7990			−1.34130			−0.670651	+	0.741773i	$0.733985\pi$
$462$		0			0
$463$	−2.27208			−0.105592			−0.0527962	−	0.998605i	$-0.516813\pi$
$463$	−2.27208			−0.105592			−0.0527962	+	0.998605i	$0.516813\pi$
$464$		0			0
$465$	2.17157	−	3.76127i	0.100704	−	0.174425i
$466$		0			0
$467$	−8.86396	−	15.3528i	−0.410175	−	0.710444i	0.584733	−	0.811226i	$-0.301199\pi$
$467$	−8.86396	−	15.3528i	−0.410175	−	0.710444i	−0.994909	+	0.100781i	$0.967866\pi$
$468$		0			0
$469$	−8.82843	+	21.6251i	−0.407659	+	0.998556i
$470$		0			0
$471$	7.12132	+	12.3345i	0.328133	+	0.568343i
$472$		0			0
$473$	−13.7426	+	23.8030i	−0.631887	+	1.09446i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	6.87006			0.314558
$478$		0			0
$479$	12.0355	−	20.8462i	0.549918	−	0.952485i	−0.448362	−	0.893852i	$-0.647992\pi$
$479$	12.0355	−	20.8462i	0.549918	−	0.952485i	0.998280	−	0.0586331i	$-0.0186742\pi$
$480$		0			0
$481$	−2.75736	−	4.77589i	−0.125725	−	0.217762i
$482$		0			0
$483$	2.43503	−	0.333226i	0.110798	−	0.0151623i
$484$		0			0
$485$	2.82843	+	4.89898i	0.128432	+	0.222451i
$486$		0			0
$487$	20.0711	−	34.7641i	0.909507	−	1.57531i	0.0947564	−	0.995500i	$-0.469793\pi$
$487$	20.0711	−	34.7641i	0.909507	−	1.57531i	0.814751	−	0.579812i	$-0.196874\pi$
$488$		0			0
$489$	−0.0416306			−0.00188260
$490$		0			0
$491$	40.6985			1.83670			0.918348	−	0.395773i	$-0.129523\pi$
$491$	40.6985			1.83670			0.918348	+	0.395773i	$0.129523\pi$
$492$		0			0
$493$	−3.85786	+	6.68202i	−0.173749	+	0.300943i
$494$		0			0
$495$	−6.96447	−	12.0628i	−0.313029	−	0.542183i
$496$		0			0
$497$	−42.5772	+	5.82655i	−1.90985	+	0.261357i
$498$		0			0
$499$	4.62132	+	8.00436i	0.206879	+	0.358324i	0.950730	−	0.310021i	$-0.100336\pi$
$499$	4.62132	+	8.00436i	0.206879	+	0.358324i	−0.743851	+	0.668346i	$0.767003\pi$
$500$		0			0
$501$	−6.27208	+	10.8636i	−0.280216	+	0.485348i
$502$		0			0
$503$	−3.72792			−0.166220			−0.0831099	−	0.996540i	$-0.526485\pi$
$503$	−3.72792			−0.166220			−0.0831099	+	0.996540i	$0.526485\pi$
$504$		0			0
$505$	15.4853			0.689086
$506$		0			0
$507$	3.70711	−	6.42090i	0.164638	−	0.285162i
$508$		0			0
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	7.00000	−	17.1464i	0.309662	−	0.758513i
$512$		0			0
$513$	−1.65685	−	2.86976i	−0.0731519	−	0.126703i
$514$		0			0
$515$	6.82843	−	11.8272i	0.300896	−	0.521168i
$516$		0			0
$517$	37.9706			1.66994
$518$		0			0
$519$	0.970563			0.0426030
$520$		0			0
$521$	1.05025	−	1.81909i	0.0460124	−	0.0796958i	−0.842102	−	0.539318i	$-0.818682\pi$
$521$	1.05025	−	1.81909i	0.0460124	−	0.0796958i	0.888114	+	0.459623i	$0.152015\pi$
$522$		0			0
$523$	7.65685	+	13.2621i	0.334811	+	0.579909i	0.983448	−	0.181188i	$-0.0579942\pi$
$523$	7.65685	+	13.2621i	0.334811	+	0.579909i	−0.648638	+	0.761097i	$0.724661\pi$
$524$		0			0
$525$	3.79899	+	4.89898i	0.165802	+	0.213809i
$526$		0			0
$527$	4.34315	+	7.52255i	0.189190	+	0.327687i
$528$		0			0
$529$	10.2426	−	17.7408i	0.445332	−	0.771338i
$530$		0			0
$531$	−12.8284			−0.556706
$532$		0			0
$533$	−3.31371			−0.143533
$534$		0			0
$535$	1.46447	−	2.53653i	0.0633144	−	0.109664i
$536$		0			0
$537$	3.07107	+	5.31925i	0.132526	+	0.229542i
$538$		0			0
$539$	−9.13604	+	35.5431i	−0.393517	+	1.53095i
$540$		0			0
$541$	0.428932	+	0.742932i	0.0184412	+	0.0319412i	0.875099	−	0.483944i	$-0.160796\pi$
$541$	0.428932	+	0.742932i	0.0184412	+	0.0319412i	−0.856658	+	0.515886i	$0.827463\pi$
$542$		0			0
$543$	−3.14214	+	5.44234i	−0.134842	+	0.233553i
$544$		0			0
$545$	−3.31371			−0.141944
$546$		0			0
$547$	9.55635			0.408600			0.204300	−	0.978908i	$-0.434508\pi$
$547$	9.55635			0.408600			0.204300	+	0.978908i	$0.434508\pi$
$548$		0			0
$549$	−6.64214	+	11.5045i	−0.283479	+	0.491001i
$550$		0			0
$551$	−3.29289	−	5.70346i	−0.140282	−	0.242975i
$552$		0			0
$553$	25.7782	+	33.2422i	1.09620	+	1.41360i
$554$		0			0
$555$	−2.75736	−	4.77589i	−0.117043	−	0.202725i
$556$		0			0
$557$	−9.25736	+	16.0342i	−0.392247	+	0.679392i	−0.992746	−	0.120234i	$-0.961635\pi$
$557$	−9.25736	+	16.0342i	−0.392247	+	0.679392i	0.600499	+	0.799626i	$0.294969\pi$
$558$		0			0
$559$	−3.07107			−0.129892
$560$		0			0
$561$	−3.59798			−0.151907
$562$		0			0
$563$	5.43503	−	9.41375i	0.229059	−	0.396742i	−0.728470	−	0.685077i	$-0.759768\pi$
$563$	5.43503	−	9.41375i	0.229059	−	0.396742i	0.957530	+	0.288335i	$0.0931017\pi$
$564$		0			0
$565$	−1.53553	−	2.65962i	−0.0646004	−	0.111891i
$566$		0			0
$567$	−6.02944	+	14.7690i	−0.253213	+	0.620242i
$568$		0			0
$569$	−8.65685	−	14.9941i	−0.362914	−	0.628586i	0.625525	−	0.780204i	$-0.284885\pi$
$569$	−8.65685	−	14.9941i	−0.362914	−	0.628586i	−0.988439	+	0.151618i	$0.951552\pi$
$570$		0			0
$571$	−8.34924	+	14.4613i	−0.349405	+	0.605187i	−0.986144	−	0.165892i	$-0.946950\pi$
$571$	−8.34924	+	14.4613i	−0.349405	+	0.605187i	0.636739	+	0.771079i	$0.280283\pi$
$572$		0			0
$573$	0.443651			0.0185338
$574$		0			0
$575$	−6.34315			−0.264527
$576$		0			0
$577$	−16.9142	+	29.2963i	−0.704148	+	1.21962i	0.262850	+	0.964837i	$0.415337\pi$
$577$	−16.9142	+	29.2963i	−0.704148	+	1.21962i	−0.966998	+	0.254783i	$0.917996\pi$
$578$		0			0
$579$	1.82843	+	3.16693i	0.0759868	+	0.131613i
$580$		0			0
$581$	−12.8431	+	1.75754i	−0.532823	+	0.0729152i
$582$		0			0
$583$	6.77817	+	11.7401i	0.280723	+	0.486227i
$584$		0			0
$585$	0.778175	−	1.34784i	0.0321736	−	0.0557262i
$586$		0			0
$587$	−34.0000			−1.40333			−0.701665	−	0.712507i	$-0.747560\pi$
$587$	−34.0000			−1.40333			−0.701665	+	0.712507i	$0.747560\pi$
$588$		0			0
$589$	−7.41421			−0.305497
$590$		0			0
$591$	5.12132	−	8.87039i	0.210663	−	0.364879i
$592$		0			0
$593$	9.15685	+	15.8601i	0.376027	+	0.651298i	0.990480	−	0.137655i	$-0.0439567\pi$
$593$	9.15685	+	15.8601i	0.376027	+	0.651298i	−0.614453	+	0.788953i	$0.710623\pi$
$594$		0			0
$595$	3.07107	−	0.420266i	0.125902	−	0.0172292i
$596$		0			0
$597$	3.53553	+	6.12372i	0.144700	+	0.250627i
$598$		0			0
$599$	10.6066	−	18.3712i	0.433374	−	0.750626i	−0.563787	−	0.825920i	$-0.690656\pi$
$599$	10.6066	−	18.3712i	0.433374	−	0.750626i	0.997161	+	0.0752942i	$0.0239896\pi$
$600$		0			0
$601$	48.5269			1.97945			0.989727	−	0.142970i	$-0.0456653\pi$
$601$	48.5269			1.97945			0.989727	+	0.142970i	$0.0456653\pi$
$602$		0			0
$603$	−23.4558			−0.955196
$604$		0			0
$605$	8.24264	−	14.2767i	0.335111	−	0.580429i
$606$		0			0
$607$	1.94975	+	3.37706i	0.0791378	+	0.137071i	0.902878	−	0.429896i	$-0.141450\pi$
$607$	1.94975	+	3.37706i	0.0791378	+	0.137071i	−0.823740	+	0.566967i	$0.808117\pi$
$608$		0			0
$609$	3.85786	−	9.44980i	0.156329	−	0.382925i
$610$		0			0
$611$	2.12132	+	3.67423i	0.0858194	+	0.148644i
$612$		0			0
$613$	7.75736	−	13.4361i	0.313317	−	0.542681i	−0.665761	−	0.746165i	$-0.731893\pi$
$613$	7.75736	−	13.4361i	0.313317	−	0.542681i	0.979078	+	0.203484i	$0.0652265\pi$
$614$		0			0
$615$	−3.31371			−0.133622
$616$		0			0
$617$	−29.2843			−1.17894			−0.589470	−	0.807790i	$-0.700663\pi$
$617$	−29.2843			−1.17894			−0.589470	+	0.807790i	$0.700663\pi$
$618$		0			0
$619$	−14.4497	+	25.0277i	−0.580784	+	1.00595i	0.414602	+	0.910003i	$0.363921\pi$
$619$	−14.4497	+	25.0277i	−0.580784	+	1.00595i	−0.995387	+	0.0959453i	$0.969413\pi$
$620$		0			0
$621$	2.62742	+	4.55082i	0.105435	+	0.182618i
$622$		0			0
$623$	28.4645	+	36.7063i	1.14040	+	1.47061i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	1.53553	−	2.65962i	0.0613233	−	0.106215i
$628$		0			0
$629$	11.0294			0.439772
$630$		0			0
$631$	19.3848			0.771696			0.385848	−	0.922562i	$-0.373909\pi$
$631$	19.3848			0.771696			0.385848	+	0.922562i	$0.373909\pi$
$632$		0			0
$633$	4.72792	−	8.18900i	0.187918	−	0.325484i
$634$		0			0
$635$	5.77817	+	10.0081i	0.229300	+	0.397159i
$636$		0			0
$637$	−3.94975	+	1.10165i	−0.156495	+	0.0436490i
$638$		0			0
$639$	−21.5772	−	37.3727i	−0.853579	−	1.47844i
$640$		0			0
$641$	−16.6569	+	28.8505i	−0.657906	+	1.13953i	0.323251	+	0.946313i	$0.395224\pi$
$641$	−16.6569	+	28.8505i	−0.657906	+	1.13953i	−0.981157	+	0.193214i	$0.938109\pi$
$642$		0			0
$643$	44.4853			1.75433			0.877164	−	0.480191i	$-0.159433\pi$
$643$	44.4853			1.75433			0.877164	+	0.480191i	$0.159433\pi$
$644$		0			0
$645$	−3.07107			−0.120923
$646$		0			0
$647$	−21.0355	+	36.4346i	−0.826992	+	1.43239i	0.0733950	+	0.997303i	$0.476617\pi$
$647$	−21.0355	+	36.4346i	−0.826992	+	1.43239i	−0.900387	+	0.435090i	$0.856717\pi$
$648$		0			0
$649$	−12.6569	−	21.9223i	−0.496825	−	0.860526i
$650$		0			0
$651$	−7.04163	−	9.08052i	−0.275983	−	0.355894i
$652$		0			0
$653$	0.928932	+	1.60896i	0.0363519	+	0.0629634i	0.883629	−	0.468188i	$-0.155093\pi$
$653$	0.928932	+	1.60896i	0.0363519	+	0.0629634i	−0.847277	+	0.531151i	$0.821760\pi$
$654$		0			0
$655$	−4.82843	+	8.36308i	−0.188662	+	0.326773i
$656$		0			0
$657$	18.5980			0.725576
$658$		0			0
$659$	−12.3848			−0.482442			−0.241221	−	0.970470i	$-0.577548\pi$
$659$	−12.3848			−0.482442			−0.241221	+	0.970470i	$0.577548\pi$
$660$		0			0
$661$	22.4350	−	38.8586i	0.872621	−	1.51142i	0.0133464	−	0.999911i	$-0.495752\pi$
$661$	22.4350	−	38.8586i	0.872621	−	1.51142i	0.859275	−	0.511514i	$-0.170915\pi$
$662$		0			0
$663$	−0.201010	−	0.348160i	−0.00780659	−	0.0135214i
$664$		0			0
$665$	−1.00000	+	2.44949i	−0.0387783	+	0.0949871i
$666$		0			0
$667$	5.22183	+	9.04447i	0.202190	+	0.350203i
$668$		0			0
$669$	2.27208	−	3.93535i	0.0878436	−	0.152150i
$670$		0			0
$671$	−26.2132			−1.01195
$672$		0			0
$673$	4.62742			0.178374			0.0891869	−	0.996015i	$-0.471573\pi$
$673$	4.62742			0.178374			0.0891869	+	0.996015i	$0.471573\pi$
$674$		0			0
$675$	−6.62742	+	11.4790i	−0.255089	+	0.441828i
$676$		0			0
$677$	5.65685	+	9.79796i	0.217411	+	0.376566i	0.954016	−	0.299757i	$-0.0969056\pi$
$677$	5.65685	+	9.79796i	0.217411	+	0.376566i	−0.736605	+	0.676323i	$0.763572\pi$
$678$		0			0
$679$	14.8284	−	2.02922i	0.569063	−	0.0778745i
$680$		0			0
$681$	0.414214	+	0.717439i	0.0158727	+	0.0274923i
$682$		0			0
$683$	−2.07107	+	3.58719i	−0.0792472	+	0.137260i	−0.902925	−	0.429797i	$-0.858585\pi$
$683$	−2.07107	+	3.58719i	−0.0792472	+	0.137260i	0.823678	+	0.567058i	$0.191918\pi$
$684$		0			0
$685$	10.6569			0.407177
$686$		0			0
$687$	9.37258			0.357586
$688$		0			0
$689$	−0.757359	+	1.31178i	−0.0288531	+	0.0499750i
$690$		0			0
$691$	−14.3137	−	24.7921i	−0.544519	−	0.943135i	−0.998637	−	0.0521932i	$-0.983379\pi$
$691$	−14.3137	−	24.7921i	−0.544519	−	0.943135i	0.454118	−	0.890942i	$-0.349954\pi$
$692$		0			0
$693$	−36.5122	+	4.99658i	−1.38698	+	0.189804i
$694$		0			0
$695$	6.27817	+	10.8741i	0.238145	+	0.412479i
$696$		0			0
$697$	3.31371	−	5.73951i	0.125516	−	0.217399i
$698$		0			0
$699$	−10.3431			−0.391214
$700$		0			0
$701$	18.7990			0.710028			0.355014	−	0.934861i	$-0.384476\pi$
$701$	18.7990			0.710028			0.355014	+	0.934861i	$0.384476\pi$
$702$		0			0
$703$	−4.70711	+	8.15295i	−0.177532	+	0.307494i
$704$		0			0
$705$	2.12132	+	3.67423i	0.0798935	+	0.138380i
$706$		0			0
$707$	15.4853	−	37.9310i	0.582384	−	1.42654i
$708$		0			0
$709$	13.2990	+	23.0345i	0.499454	+	0.865080i	1.00000		0.000630296i	$-0.000200629\pi$
$709$	13.2990	+	23.0345i	0.499454	+	0.865080i	−0.500546	+	0.865710i	$0.666867\pi$
$710$		0			0
$711$	−21.1213	+	36.5832i	−0.792111	+	1.37198i
$712$		0			0
$713$	11.7574			0.440317
$714$		0			0
$715$	3.07107			0.114851
$716$		0			0
$717$	4.58579	−	7.94282i	0.171259	−	0.296630i
$718$		0			0
$719$	9.65685	+	16.7262i	0.360140	+	0.623781i	0.987984	−	0.154559i	$-0.0493956\pi$
$719$	9.65685	+	16.7262i	0.360140	+	0.623781i	−0.627844	+	0.778339i	$0.716062\pi$
$720$		0			0
$721$	−22.1421	−	28.5533i	−0.824616	−	1.06338i
$722$		0			0
$723$	4.89949	+	8.48617i	0.182214	+	0.315604i
$724$		0			0
$725$	−13.1716	+	22.8138i	−0.489180	+	0.847285i
$726$		0			0
$727$	−5.24264			−0.194439			−0.0972194	−	0.995263i	$-0.530995\pi$
$727$	−5.24264			−0.194439			−0.0972194	+	0.995263i	$0.530995\pi$
$728$		0			0
$729$	−10.1960			−0.377628
$730$		0			0
$731$	3.07107	−	5.31925i	0.113588	−	0.196739i
$732$		0			0
$733$	14.3431	+	24.8431i	0.529776	+	0.917599i	0.999397	+	0.0347309i	$0.0110574\pi$
$733$	14.3431	+	24.8431i	0.529776	+	0.917599i	−0.469621	+	0.882868i	$0.655609\pi$
$734$		0			0
$735$	−3.94975	+	1.10165i	−0.145689	+	0.0406350i
$736$		0			0
$737$	−23.1421	−	40.0834i	−0.852452	−	1.47649i
$738$		0			0
$739$	0.313708	−	0.543359i	0.0115400	−	0.0199878i	−0.860198	−	0.509961i	$-0.829660\pi$
$739$	0.313708	−	0.543359i	0.0115400	−	0.0199878i	0.871738	+	0.489973i	$0.162993\pi$
$740$		0			0
$741$	0.343146			0.0126058
$742$		0			0
$743$	46.7279			1.71428			0.857141	−	0.515083i	$-0.172239\pi$
$743$	46.7279			1.71428			0.857141	+	0.515083i	$0.172239\pi$
$744$		0			0
$745$	2.32843	−	4.03295i	0.0853070	−	0.147756i
$746$		0			0
$747$	−6.50862	−	11.2733i	−0.238138	−	0.412467i
$748$		0			0
$749$	−4.74874	−	6.12372i	−0.173515	−	0.223756i
$750$		0			0
$751$	−11.2426	−	19.4728i	−0.410250	−	0.710573i	0.584667	−	0.811273i	$-0.301225\pi$
$751$	−11.2426	−	19.4728i	−0.410250	−	0.710573i	−0.994917	+	0.100700i	$0.967892\pi$
$752$		0			0
$753$	−5.92031	+	10.2543i	−0.215748	+	0.373687i
$754$		0			0
$755$	5.65685			0.205874
$756$		0			0
$757$	−54.3137			−1.97407			−0.987033	−	0.160520i	$-0.948683\pi$
$757$	−54.3137			−1.97407			−0.987033	+	0.160520i	$0.948683\pi$
$758$		0			0
$759$	−2.43503	+	4.21759i	−0.0883859	+	0.153089i
$760$		0			0
$761$	−7.57107	−	13.1135i	−0.274451	−	0.475363i	0.695545	−	0.718482i	$-0.255163\pi$
$761$	−7.57107	−	13.1135i	−0.274451	−	0.475363i	−0.969996	+	0.243119i	$0.921829\pi$
$762$		0			0
$763$	−3.31371	+	8.11689i	−0.119964	+	0.293851i
$764$		0			0
$765$	1.55635	+	2.69568i	0.0562699	+	0.0974624i
$766$		0			0
$767$	1.41421	−	2.44949i	0.0510643	−	0.0884459i
$768$		0			0
$769$	−54.4558			−1.96373			−0.981864	−	0.189587i	$-0.939285\pi$
$769$	−54.4558			−1.96373			−0.981864	+	0.189587i	$0.939285\pi$
$770$		0			0
$771$	8.20101			0.295352
$772$		0			0
$773$	7.53553	−	13.0519i	0.271034	−	0.469445i	−0.698093	−	0.716007i	$-0.745968\pi$
$773$	7.53553	−	13.0519i	0.271034	−	0.469445i	0.969127	+	0.246562i	$0.0793010\pi$
$774$		0			0
$775$	14.8284	+	25.6836i	0.532653	+	0.922582i
$776$		0			0
$777$	−14.4558	+	1.97824i	−0.518601	+	0.0709689i
$778$		0			0
$779$	2.82843	+	4.89898i	0.101339	+	0.175524i
$780$		0			0
$781$	42.5772	−	73.7458i	1.52353	−	2.63883i
$782$		0			0
$783$	21.8234			0.779904
$784$		0			0
$785$	24.3137			0.867793
$786$		0			0
$787$	−10.1213	+	17.5306i	−0.360786	+	0.624900i	−0.988090	−	0.153874i	$-0.950825\pi$
$787$	−10.1213	+	17.5306i	−0.360786	+	0.624900i	0.627304	+	0.778774i	$0.284158\pi$
$788$		0			0
$789$	7.85786	+	13.6102i	0.279747	+	0.484537i
$790$		0			0
$791$	−8.05025	+	1.10165i	−0.286234	+	0.0391702i
$792$		0			0
$793$	−1.46447	−	2.53653i	−0.0520047	−	0.0900748i
$794$		0			0
$795$	−0.757359	+	1.31178i	−0.0268608	+	0.0465242i
$796$		0			0
$797$	53.4975			1.89498			0.947489	−	0.319789i	$-0.103612\pi$
$797$	53.4975			1.89498			0.947489	+	0.319789i	$0.103612\pi$
$798$		0			0
$799$	−8.48528			−0.300188
$800$		0			0
$801$	−23.3223	+	40.3955i	−0.824054	+	1.42730i
$802$		0			0
$803$	18.3492	+	31.7818i	0.647531	+	1.12156i
$804$		0			0
$805$	1.58579	−	3.88437i	0.0558916	−	0.136906i
$806$		0			0
$807$	4.68629	+	8.11689i	0.164965	+	0.285728i
$808$		0			0
$809$	−2.98528	+	5.17066i	−0.104957	+	0.181791i	−0.913721	−	0.406343i	$-0.866804\pi$
$809$	−2.98528	+	5.17066i	−0.104957	+	0.181791i	0.808764	+	0.588134i	$0.200137\pi$
$810$		0			0
$811$	−52.4264			−1.84094			−0.920470	−	0.390813i	$-0.872194\pi$
$811$	−52.4264			−1.84094			−0.920470	+	0.390813i	$0.872194\pi$
$812$		0			0
$813$	16.2426			0.569654
$814$		0			0
$815$	−0.0355339	+	0.0615465i	−0.00124470	+	0.00215588i
$816$		0			0
$817$	2.62132	+	4.54026i	0.0917084	+	0.158844i
$818$		0			0
$819$	−2.52334	−	3.25397i	−0.0881727	−	0.113703i
$820$		0			0
$821$	−20.9853	−	36.3476i	−0.732391	−	1.26854i	−0.955858	−	0.293828i	$-0.905071\pi$
$821$	−20.9853	−	36.3476i	−0.732391	−	1.26854i	0.223467	−	0.974711i	$-0.428262\pi$
$822$		0			0
$823$	7.86396	−	13.6208i	0.274120	−	0.474791i	−0.695792	−	0.718243i	$-0.744947\pi$
$823$	7.86396	−	13.6208i	0.274120	−	0.474791i	0.969913	+	0.243452i	$0.0782800\pi$
$824$		0			0
$825$	−12.2843			−0.427683
$826$		0			0
$827$	−23.3137			−0.810697			−0.405349	−	0.914162i	$-0.632850\pi$
$827$	−23.3137			−0.810697			−0.405349	+	0.914162i	$0.632850\pi$
$828$		0			0
$829$	−8.34315	+	14.4508i	−0.289769	+	0.501895i	−0.973755	−	0.227601i	$-0.926912\pi$
$829$	−8.34315	+	14.4508i	−0.289769	+	0.501895i	0.683985	+	0.729496i	$0.260245\pi$
$830$		0			0
$831$	−1.74874	−	3.02890i	−0.0606630	−	0.105071i
$832$		0			0
$833$	2.04163	−	7.94282i	0.0707383	−	0.275202i
$834$		0			0
$835$	10.7071	+	18.5453i	0.370535	+	0.641785i
$836$		0			0
$837$	12.2843	−	21.2770i	0.424607	−	0.735440i
$838$		0			0
$839$	13.5147			0.466580			0.233290	−	0.972407i	$-0.425051\pi$
$839$	13.5147			0.466580			0.233290	+	0.972407i	$0.425051\pi$
$840$		0			0
$841$	14.3726			0.495606
$842$		0			0
$843$	−0.556349	+	0.963625i	−0.0191617	+	0.0331890i
$844$		0			0
$845$	−6.32843	−	10.9612i	−0.217705	−	0.377075i
$846$		0			0
$847$	−26.7279	−	34.4669i	−0.918382	−	1.18430i
$848$		0			0
$849$	4.84924	+	8.39913i	0.166426	+	0.288258i
$850$		0			0
$851$	7.46447	−	12.9288i	0.255879	−	0.443195i
$852$		0			0
$853$	−1.54416			−0.0528709			−0.0264354	−	0.999651i	$-0.508416\pi$
$853$	−1.54416			−0.0528709			−0.0264354	+	0.999651i	$0.508416\pi$
$854$		0			0
$855$	−2.65685			−0.0908625
$856$		0			0
$857$	−20.4853	+	35.4815i	−0.699764	+	1.21203i	0.268784	+	0.963200i	$0.413378\pi$
$857$	−20.4853	+	35.4815i	−0.699764	+	1.21203i	−0.968548	+	0.248826i	$0.919955\pi$
$858$		0			0
$859$	−24.5919	−	42.5944i	−0.839064	−	1.45330i	−0.890678	−	0.454635i	$-0.849770\pi$
$859$	−24.5919	−	42.5944i	−0.839064	−	1.45330i	0.0516137	−	0.998667i	$-0.483564\pi$
$860$		0			0
$861$	−3.31371	+	8.11689i	−0.112931	+	0.276623i
$862$		0			0
$863$	−14.4350	−	25.0022i	−0.491374	−	0.851085i	0.508577	−	0.861017i	$-0.330172\pi$
$863$	−14.4350	−	25.0022i	−0.491374	−	0.851085i	−0.999951	+	0.00993186i	$0.996839\pi$
$864$		0			0
$865$	0.828427	−	1.43488i	0.0281674	−	0.0487873i
$866$		0			0
$867$	−9.15433			−0.310897
$868$		0			0
$869$	−83.3553			−2.82764
$870$		0			0
$871$	2.58579	−	4.47871i	0.0876160	−	0.151755i
$872$		0			0
$873$	7.51472	+	13.0159i	0.254335	+	0.440521i
$874$		0			0
$875$	23.5919	−	3.22848i	0.797551	−	0.109142i
$876$		0			0
$877$	8.43503	+	14.6099i	0.284831	+	0.493341i	0.972568	−	0.232618i	$-0.0747293\pi$
$877$	8.43503	+	14.6099i	0.284831	+	0.493341i	−0.687737	+	0.725960i	$0.741396\pi$
$878$		0			0
$879$	0.485281	−	0.840532i	0.0163681	−	0.0283504i
$880$		0			0
$881$	−15.3137			−0.515932			−0.257966	−	0.966154i	$-0.583052\pi$
$881$	−15.3137			−0.515932			−0.257966	+	0.966154i	$0.583052\pi$
$882$		0			0
$883$	−30.8284			−1.03746			−0.518730	−	0.854938i	$-0.673595\pi$
$883$	−30.8284			−1.03746			−0.518730	+	0.854938i	$0.673595\pi$
$884$		0			0
$885$	1.41421	−	2.44949i	0.0475383	−	0.0823387i
$886$		0			0
$887$	−14.1421	−	24.4949i	−0.474846	−	0.822458i	0.524739	−	0.851263i	$-0.324163\pi$
$887$	−14.1421	−	24.4949i	−0.474846	−	0.822458i	−0.999585	+	0.0288053i	$0.990830\pi$
$888$		0			0
$889$	30.2929	−	4.14549i	1.01599	−	0.139035i
$890$		0			0
$891$	−15.8051	−	27.3752i	−0.529490	−	0.917104i
$892$		0			0
$893$	3.62132	−	6.27231i	0.121183	−	0.209895i
$894$		0			0
$895$	10.4853			0.350484
$896$		0			0
$897$	−0.544156			−0.0181688
$898$		0			0
$899$	24.4142	−	42.2867i	0.814260	−	1.41034i
$900$		0			0
$901$	−1.51472	−	2.62357i	−0.0504626	−	0.0874038i
$902$		0			0
$903$	−3.07107	+	7.52255i	−0.102199	+	0.250335i
$904$		0			0
$905$	5.36396	+	9.29065i	0.178304	+	0.308832i
$906$		0			0
$907$	9.22183	−	15.9727i	0.306206	−	0.530364i	−0.671323	−	0.741165i	$-0.734274\pi$
$907$	9.22183	−	15.9727i	0.306206	−	0.530364i	0.977529	+	0.210801i	$0.0676071\pi$
$908$		0			0
$909$	41.1421			1.36460
$910$		0			0
$911$	5.55635			0.184090			0.0920450	−	0.995755i	$-0.470660\pi$
$911$	5.55635			0.184090			0.0920450	+	0.995755i	$0.470660\pi$
$912$		0			0
$913$	12.8431	−	22.2450i	0.425046	−	0.736201i
$914$		0			0
$915$	−1.46447	−	2.53653i	−0.0484138	−	0.0838551i
$916$		0			0
$917$	15.6569	+	20.1903i	0.517035	+	0.666741i
$918$		0			0
$919$	−4.20711	−	7.28692i	−0.138780	−	0.240373i	0.788255	−	0.615348i	$-0.210985\pi$
$919$	−4.20711	−	7.28692i	−0.138780	−	0.240373i	−0.927035	+	0.374975i	$0.877651\pi$
$920$		0			0
$921$	7.79899	−	13.5082i	0.256985	−	0.445112i
$922$		0			0
$923$	9.51472			0.313181
$924$		0			0
$925$	37.6569			1.23815
$926$		0			0
$927$	18.1421	−	31.4231i	0.595866	−	1.03207i
$928$		0			0
$929$	−4.81371	−	8.33759i	−0.157933	−	0.273547i	0.776190	−	0.630499i	$-0.217150\pi$
$929$	−4.81371	−	8.33759i	−0.157933	−	0.273547i	−0.934123	+	0.356951i	$0.883816\pi$
$930$		0			0
$931$	5.00000	+	4.89898i	0.163868	+	0.160558i
$932$		0			0
$933$	−2.34315	−	4.05845i	−0.0767111	−	0.132868i
$934$		0			0
$935$	−3.07107	+	5.31925i	−0.100435	+	0.173958i
$936$		0			0
$937$	47.4853			1.55128			0.775638	−	0.631178i	$-0.217428\pi$
$937$	47.4853			1.55128			0.775638	+	0.631178i	$0.217428\pi$
$938$		0			0
$939$	−15.8995			−0.518860
$940$		0			0
$941$	−12.2929	+	21.2919i	−0.400737	+	0.694097i	−0.993815	−	0.111048i	$-0.964579\pi$
$941$	−12.2929	+	21.2919i	−0.400737	+	0.694097i	0.593078	+	0.805145i	$0.297913\pi$
$942$		0			0
$943$	−4.48528	−	7.76874i	−0.146061	−	0.252985i
$944$		0			0
$945$	−5.37258	−	6.92820i	−0.174770	−	0.225374i
$946$		0			0
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	0.996178	−	0.0873481i	$-0.0278392\pi$
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	−0.573735	+	0.819041i	$0.694506\pi$
$948$		0			0
$949$	−2.05025	+	3.55114i	−0.0665540	+	0.115275i
$950$		0			0
$951$	−1.02944			−0.0333818
$952$		0			0
$953$	51.1543			1.65705			0.828526	−	0.559951i	$-0.189180\pi$
$953$	51.1543			1.65705			0.828526	+	0.559951i	$0.189180\pi$
$954$		0			0
$955$	0.378680	−	0.655892i	0.0122538	−	0.0212242i
$956$		0			0
$957$	10.1127	+	17.5157i	0.326897	+	0.566202i
$958$		0			0
$959$	10.6569	−	26.1039i	0.344128	−	0.842937i
$960$		0			0
$961$	−11.9853	−	20.7591i	−0.386622	−	0.669649i
$962$		0			0
$963$	3.89087	−	6.73919i	0.125382	−	0.217167i
$964$		0			0
$965$	6.24264			0.200958
$966$		0			0
$967$	−16.9706			−0.545737			−0.272868	−	0.962051i	$-0.587972\pi$
$967$	−16.9706			−0.545737			−0.272868	+	0.962051i	$0.587972\pi$
$968$		0			0
$969$	−0.343146	+	0.594346i	−0.0110234	+	0.0190931i
$970$		0			0
$971$	2.43503	+	4.21759i	0.0781438	+	0.135349i	0.902449	−	0.430797i	$-0.141767\pi$
$971$	2.43503	+	4.21759i	0.0781438	+	0.135349i	−0.824305	+	0.566146i	$0.808434\pi$
$972$		0			0
$973$	32.9142	−	4.50421i	1.05518	−	0.144398i
$974$		0			0
$975$	−0.686292	−	1.18869i	−0.0219789	−	0.0380686i
$976$		0			0
$977$	2.65685	−	4.60181i	0.0850003	−	0.147225i	−0.820391	−	0.571803i	$-0.806244\pi$
$977$	2.65685	−	4.60181i	0.0850003	−	0.147225i	0.905391	+	0.424578i	$0.139578\pi$
$978$		0			0
$979$	−92.0416			−2.94166
$980$		0			0
$981$	−8.80404			−0.281091
$982$		0			0
$983$	−8.97056	+	15.5375i	−0.286117	+	0.495568i	−0.972879	−	0.231313i	$-0.925698\pi$
$983$	−8.97056	+	15.5375i	−0.286117	+	0.495568i	0.686763	+	0.726882i	$0.259031\pi$
$984$		0			0
$985$	−8.74264	−	15.1427i	−0.278564	−	0.482486i
$986$		0			0
$987$	11.1213	−	1.52192i	0.353996	−	0.0484432i
$988$		0			0
$989$	−4.15685	−	7.19988i	−0.132180	−	0.228943i
$990$		0			0
$991$	−3.72792	+	6.45695i	−0.118421	+	0.205112i	−0.919142	−	0.393926i	$-0.871117\pi$
$991$	−3.72792	+	6.45695i	−0.118421	+	0.205112i	0.800721	+	0.599038i	$0.204450\pi$
$992$		0			0
$993$	−0.887302			−0.0281577
$994$		0			0
$995$	12.0711			0.382679
$996$		0			0
$997$	29.7990	−	51.6134i	0.943743	−	1.63461i	0.185496	−	0.982645i	$-0.440611\pi$
$997$	29.7990	−	51.6134i	0.943743	−	1.63461i	0.758248	−	0.651967i	$-0.226056\pi$
$998$		0			0
$999$	−15.5980	−	27.0165i	−0.493498	−	0.854764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.k.305.2	✓	4
7.2	even	3	inner	1064.2.q.k.457.2	yes	4
7.3	odd	6		7448.2.a.x.1.2		2
7.4	even	3		7448.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.k.305.2	✓	4	1.1	even	1	trivial
1064.2.q.k.457.2	yes	4	7.2	even	3	inner
7448.2.a.x.1.2		2	7.3	odd	6
7448.2.a.bd.1.1		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 + 0.507306i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.32843 + 2.30090i) q^{9} +O(q^{10})\)	\(q+(-0.292893 + 0.507306i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.32843 + 2.30090i) q^{9} +(-2.62132 + 4.54026i) q^{11} -0.585786 q^{13} -0.585786 q^{15} +(0.585786 - 1.01461i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-0.585786 + 1.43488i) q^{21} +(-0.792893 - 1.37333i) q^{23} +(2.00000 - 3.46410i) q^{25} -3.31371 q^{27} -6.58579 q^{29} +(-3.70711 + 6.42090i) q^{31} +(-1.53553 - 2.65962i) q^{33} +(1.62132 + 2.09077i) q^{35} +(4.70711 + 8.15295i) q^{37} +(0.171573 - 0.297173i) q^{39} +5.65685 q^{41} +5.24264 q^{43} +(-1.32843 + 2.30090i) q^{45} +(-3.62132 - 6.27231i) q^{47} +(6.74264 - 1.88064i) q^{49} +(0.343146 + 0.594346i) q^{51} +(1.29289 - 2.23936i) q^{53} -5.24264 q^{55} -0.585786 q^{57} +(-2.41421 + 4.18154i) q^{59} +(2.50000 + 4.33013i) q^{61} +(4.30761 + 5.55487i) q^{63} +(-0.292893 - 0.507306i) q^{65} +(-4.41421 + 7.64564i) q^{67} +0.928932 q^{69} -16.2426 q^{71} +(3.50000 - 6.06218i) q^{73} +(1.17157 + 2.02922i) q^{75} +(-5.24264 + 12.8418i) q^{77} +(7.94975 + 13.7694i) q^{79} +(-3.01472 + 5.22165i) q^{81} -4.89949 q^{83} +1.17157 q^{85} +(1.92893 - 3.34101i) q^{87} +(8.77817 + 15.2042i) q^{89} +(-1.53553 + 0.210133i) q^{91} +(-2.17157 - 3.76127i) q^{93} +(-0.500000 + 0.866025i) q^{95} +5.65685 q^{97} -13.9289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 4 q - 4 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 2 q^{11} - 8 q^{13} - 8 q^{15} + 8 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{23} + 8 q^{25} + 32 q^{27} - 32 q^{29} - 12 q^{31} + 8 q^{33} - 2 q^{35} + 16 q^{37} + 12 q^{39} + 4 q^{43} + 6 q^{45} - 6 q^{47} + 10 q^{49} + 24 q^{51} + 8 q^{53} - 4 q^{55} - 8 q^{57} - 4 q^{59} + 10 q^{61} + 54 q^{63} - 4 q^{65} - 12 q^{67} + 32 q^{69} - 48 q^{71} + 14 q^{73} + 16 q^{75} - 4 q^{77} + 12 q^{79} - 46 q^{81} + 20 q^{83} + 16 q^{85} + 36 q^{87} + 4 q^{89} + 8 q^{91} - 20 q^{93} - 2 q^{95} - 84 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 2 * q^11 - 8 * q^13 - 8 * q^15 + 8 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^23 + 8 * q^25 + 32 * q^27 - 32 * q^29 - 12 * q^31 + 8 * q^33 - 2 * q^35 + 16 * q^37 + 12 * q^39 + 4 * q^43 + 6 * q^45 - 6 * q^47 + 10 * q^49 + 24 * q^51 + 8 * q^53 - 4 * q^55 - 8 * q^57 - 4 * q^59 + 10 * q^61 + 54 * q^63 - 4 * q^65 - 12 * q^67 + 32 * q^69 - 48 * q^71 + 14 * q^73 + 16 * q^75 - 4 * q^77 + 12 * q^79 - 46 * q^81 + 20 * q^83 + 16 * q^85 + 36 * q^87 + 4 * q^89 + 8 * q^91 - 20 * q^93 - 2 * q^95 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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